Combining low poly cone and disc
I for myself always try to connect objects in "a clean way" whenever possible but there are many cases where objects just won't fit in a way that justifies the effort for the sake of that rule. 

While you can certainly split your geometry on both objects it's not the best thing to do here, because


you will increase your vertex count unnecessarily nonetheless
your topology won't get cleaner.


In the case of your model I'd just keep the objects as they are. If however you still want them to be connected I would rotate the disk so that the cone meets a flat part of the disk's edge and then rotate the cone so that the loop cut of the disk hits one of the cone's edges. It then should be at least a little easier to connect both pieces.